Issue 50

G. Belokas, Frattura ed Integrità Strutturale, 50 (2019) 354-369; DOI: 10.3221/IGF-ESIS.50.30

Finally, as it was applied for the direct shear test, a common approach in engineering practice for the estimation of all stat istical measures of c and tan φ is first to derive the Mohr – Coulomb constants ( c , tan φ ) for each sample separately (see Table 4) and then apply a statistical t-test on each constant independently for n /3-1 dof (where n the complete number of specimens and n /3 the number of specific locations of soil sampling). For the Herakleion marl case the n /3-1=8 dof lead to: a) mean values: c m =64.34kPa, (tan φ ) m =0.59415, b) standard deviation: S d,c =55.69kPa, S d,tanφ =0.13577, c) standard error:

Figure 7 : Characteristic and best estimate Mohr – Coulomb failure envelopes superimposed on the Mohr – Coulomb failure envelopes of each sample.

c m

(tan φ ) m

SE c

SE tan(φ)

Best estimate

(kPa)

(kPa)

a m c m

, b m

from linear regression of all σ 1 , σ 3

data points

, (tan φ ) m

from Eqs.(20,19)

66.00

0.58225

15.50

0.0347

and SE tanφ

from FORM error propagation

SE c

(this gives characteristic 1)

c m

, (tan φ ) m

from mean values of Table 4 from single variable model

SE c

and SE tanφ

64.34

0.59415

18.56

0.0423

(this gives characteristic 4)

Table 5 : Mohr – Coulomb failure criterion constants (mean values and uncertainties).

c k

(tan φ ) k

Characteristic values

(kPa)

Characteristic 1 ( SE from FORM error propagation): c k = c m - t p,n-2 SE c , tan( φ ) k = tan( φ ) m - t p,n-2 SE tan(φ)

39.60

0.52297

Characteristic 2: a k , b k

55.65

0.56288

from linear regression on σ 1pred

, σ 3

data points ( σ 1pred

= a m

+ σ 3

b m

± t n-2

SE σ1

)

c k

, (tan φ ) k

from Eqs.(20,19)

Characteristic 3: a k = a m - t p,n-2 SE a , b k

43.43

0.49395

= b m

- t p,n-2

SE b

c k

, (tan φ ) k

from Eqs.(20,19)

Characteristic 4 ( SE from one variable model, Eq.(4), for c and tan φ ): cm and tanφ from mean values of Table 4 c k = c m - t p,n-2 SE c , tan( φ ) k = tan( φ ) m - t p,n-2 SE tan(φ)

29.82

0.50990

Table 6 : Mohr – Coulomb failure criterion constants (characteristic values).

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